Example

Just as for the whole numbers, is greater than means is to the right on the number line. Similarly , is less than means is to the left on the number line. Notice that 22/7 is greater than 2 1/4 because it is to the right on the number line. 4/5 is less than 7/4 and is to the left on the number line.

Exercise

Choose which inequality or equality sign makes the statement true:

If a, d
are both positive, there is an alternative method of solving these problems that does
not involve computing a common denominator.

Exercise

Using this method try some more exercises.

Look again at the number line, including negative fractions.

When negative and positive fractions are compared, the situation is easy. Any positive number is greater than a negative number. This applies to fractions as well as integers. Positive numbers are always on the right on a number line and negative numbers on the left. For example ½ > −2¼.

When two negative fractions are compared using the common denominator method, the smaller numerator belongs to the greater fraction . For example −¼ > −¾ or −1/2 > −4/5 because −1/2 = -5/10 whereas −4/5 = -8/10. The same thing applies to negative mixed numbers. for example −1¼ > −3¾.